1. Field of the Invention
This invention relates to a device and method of rotating an optical element, such as a diffraction grating for dispersing light of various wavelengths, whereby the optical element is rotated on an axis of rotation that does not intersect a point on the surface of the diffraction grating The invention is especially useful in a spectrophotometer.
2. Description of the Prior Art
The use of diffraction gratings of various configurations is common for dispersing a portion of the electromagnetic spectrum, for use for instance in spectrophotometers One method of selecting the wavelength being directed from the radiation source to a given destination point is by rotating the diffraction grating. The angular position of the diffraction grating to yield a given wavelength at the destination is easily determined and theoretically predictable for a given diffraction grating and angle of incident light from the source and of diffracted light to the destination, if the axis of rotation passes through a point on the surface of the diffraction grating.
In the conventional use (see FIG. 1) of a diffraction grating 10 on the surface of substrate 11 for wavelength selection, the relationship for wavelength as a function of grating position is shown in FIG. 1 and in equation A where .lambda. is the wavelength, N is the groove density of the diffraction grating (not shown), K is an integer for the diffraction order (the order of interest is typically 1), .alpha. is angle of incidence, and .beta. is the angle of diffraction. EQU KN.lambda.=SIN .alpha.+SIN .beta. (A)
The angles of incidence and diffraction are measured from a line between the light source 12 and light destination 14 respectively to the point where the axis of rotation 16 intersects the grating 10 to the normal 19 to the grating 10 at this same point. Counterclockwise angles are shown as positive in FIG. 1. Using a trigonometric identity, equation A is rewritten as equation B. ##EQU1## Thus, for a system where the angle between the source 12 and destination 14 is fixed and the grating 10 is rotated, both .alpha. and .beta. would be changing, but the quantity .alpha. minus .beta. will remain constant and is given by .theta. in equation C. EQU .theta.=.alpha.-.beta. (B)
With .lambda., N and K constant, equation B is solved for .alpha. plus .beta. as in equation D. ##EQU2## Then equations C and D are solved simultaneously for .alpha. and .beta. resulting in the required position of the grating 10. However, the diffraction grating position for rotation of the grating 10 about an axis not passing through a point on the grating 10 cannot be solved in this manner since the equations are much more complex.
Hence, in the prior art, gratings are typically rotated on axes passing through a point on the grating 10 so as to permit easy determination of the grating positioning for each desired wavelength, and gratings are not rotated about points in the grating substrate 11.